Tetravalent Counterions Research Articles

Like-charge polymer-membrane complexation mediated by multivalent cations: One-loop-dressed strong coupling theory.

We probe the electrostatic mechanism driving adsorption of polyelectrolytes onto like-charged membranes upon the addition of tri- and tetravalent counterions to a bathing monovalent salt solution. We develop a one-loop-dressed strong coupling theory that treats the monovalent salt at the electrostatic one-loop level and the multivalent counterions within a strong-coupling approach. It is shown that the adhesive force of the multivalent counterions mediating the like-charge adsorption arises from their strong condensation at the charged membrane. The resulting interfacial counterion excess locally maximizes the screening ability of the electrolyte and minimizes the electrostatic polymer grand potential. This translates into an attractive force that pulls the polymer to the similarly charged membrane. We show that the high counterion valency enables this adsorption transition even at weakly charged membranes. Additionally, strongly charged membranes give rise to monovalent counterion-induced correlations and intensify the interfacial multivalent counterion condensation, strengthening the complexation of the polymer with the like-charged membrane, as well as triggering the orientational transition of the molecule prior to its adsorption. Finally, our theory provides two additional key features as evidenced by previous adsorption experiments: first, the critical counterion concentration for polymer adsorption decreases with the rise of the counterion valency and, second, the addition of monovalent salt enhances the screening of the membrane charges and suppresses monovalent counterion correlations close to the surface. This weakens the interfacial multivalent counterion condensation and results in the desorption of the polymer from the substrate.

Evolution of Interactions in the Protein Solution As Induced by Mono and Multivalent Ions.

The evolution of interactions in the bovine serum albumin (BSA) protein solution on addition of mono and multivalent (di, tri and tetra) counterions has been studied using small-angle neutron scattering (SANS), dynamic light scattering (DLS) and ζ-potential measurements. It is found that in the presence of mono and divalent counterions, protein behavior can be well explained by DLVO theory, combining the contributions of screened Coulomb repulsion with the van der Waals attraction. The addition of mono or divalent salts in protein solution reduces the repulsive barrier and hence the overall interaction becomes attractive, but the system remains in one-phase for the entire concentration range of the salts, added in the system. However, contrary to DLVO theory, the protein solution undergoes a reentrant phase transition from one-phase to a two-phase system and then back to the one-phase system in the presence of tri and tetravalent counterions. The results show that tri and tetravalent (unlike mono and divalent) counterions induce short-range attraction between the protein molecules, leading to the transformation from one-phase to two-phase system. The two-phase is characterized by the fractal structure of protein aggregates. The excess condensation of these higher-valent counterions in the double layer around the BSA causes the reversal of charge of the protein molecules resulting into reentrant of the one-phase, at higher salt concentrations. The complete phase behavior with mono and multivalent ions has been explained in terms of the interplay of electrostatic repulsion and ion-induced short-range attraction between the protein molecules.

DNA Compaction and Charge Neutralization Regulated by Divalent Ions in very Low pH Solution.

DNA conformation is strongly dependent on the valence of counterions in solution, and a valence of at least three is needed for DNA compaction. Recently, we directly demonstrated DNA compaction and its regulation, mediated by divalent cations, by lowering the pH of a solution. In the present study, we found that the critical electrophoretic mobility of DNA is promoted to around −1.0 × 10−4 cm2 V−1 s−1 to incur DNA compaction or condensation in a tri- and tetravalent counterions solution, corresponding to an about 89% neutralized charge fraction of DNA. This is also valid for DNA compaction by divalent counterions in a low pH solution. It is notable that the critical charge neutralization of DNA for compaction is only about 1% higher than the saturated charge fraction of DNA in a mild divalent ion solution. We also found that DNA compaction by divalent cations at low pH is weakened and even decondensed with an increasing concentration of counterions.

Morphologies of spherical polyampholyte brushes: Effects of counterion valence and charged monomer sequence

We study the conformational behavior of spherical brushes composed of polyampholyte chains end-grafted onto spherical particles in the presence of monovalent and tetravalent counterions using molecular dynamics simulations. The overall net charge for each chain consisting of both positively and negatively charged segments is zero. The dependences of the structural properties of the brushes on the chain stiffness, grafting density and charge sequence along the chains are examined systemically. For the diblock brushes, our results indicate that increasing the chain rigidity leads to a significant effect of counterion valence and a reduced collapsing degree of the brushes. At high chain stiffness, the number of high-valent counterions trapped in the brushes is diminished compared to the cases with monovalent counterions, corresponding to lower osmotic pressure. For the flexible brushes, the short-range and electrostatic interactions depending on the charge sequence, determine the conformational transition of the brushes, whereas the effect of counterion valence becomes weaker. In the presence of high-valent counterions, the brushes which consist of polyampholyte chains with blocks of medium length, adopt a slightly stretched conformation owing to relatively strong electrostatic correlation between high-valent counterions and oppositely charged monomers.

Grand-canonical simulation of DNA condensation with two salts, effect of divalent counterion size.

The problem of DNA- DNA interaction mediated by divalent counterions is studied using a generalized grand-canonical Monte-Carlo simulation for a system of two salts. The effect of the divalent counterion size on the condensation behavior of the DNA bundle is investigated. Experimentally, it is known that multivalent counterions have strong effect on the DNA condensation phenomenon. While tri- and tetra-valent counterions are shown to easily condense free DNA molecules in solution into toroidal bundles, the situation with divalent counterions is not as clear cut. Some divalent counterions like Mg(+2) are not able to condense free DNA molecules in solution, while some like Mn(+2) can condense them into disorder bundles. In restricted environment such as in two dimensional system or inside viral capsid, Mg(+2) can have strong effect and able to condense them, but the condensation varies qualitatively with different system, different coions. It has been suggested that divalent counterions can induce attraction between DNA molecules but the strength of the attraction is not strong enough to condense free DNA in solution. However, if the configuration entropy of DNA is restricted, these attractions are enough to cause appreciable effects. The variations among different divalent salts might be due to the hydration effect of the divalent counterions. In this paper, we try to understand this variation using a very simple parameter, the size of the divalent counterions. We investigate how divalent counterions with different sizes can lead to varying qualitative behavior of DNA condensation in restricted environments. Additionally, a grand canonical Monte-Carlo method for simulation of systems with two different salts is presented in detail.

Strongly correlated electrostatics of viral genome packaging

The problem of viral packaging (condensation) and ejection from viral capsid in the presence of multivalent counterions is considered. Experiments show divalent counterions strongly influence the amount of DNA ejected from bacteriophage. In this paper, the strong electrostatic interactions between DNA molecules in the presence of multivalent counterions is investigated. It is shown that experiment results agree reasonably well with the phenomenon of DNA reentrant condensation. This phenomenon is known to cause DNA condensation in the presence of tri- or tetra-valent counterions. For divalent counterions, the viral capsid confinement strongly suppresses DNA configurational entropy, therefore the correlation between divalent counterions is strongly enhanced causing similar effect. Computational studies also agree well with theoretical calculations.

Electrostatic contribution to DNA condensation—application of ‘energy minimization’ in asimple model in the strong Coulomb coupling regime

The process of bending of straight DNA to a circular form in the presence of any of themono-, di-, tri- or tetravalent counterions has been simulated in a strong Coulomb couplingenvironment, employing a previously developed energy minimization simulation technique.The inherent characteristics of the simulation technique allow the monitoring of therequired electrostatic contribution to the bending. The curvature of the bending has beenfound to play a crucial role in facilitating the electrostatic attractive potential energy. Thetotal electrostatic potential energy has been found to decrease with bending, whichindicates that bending straight DNA to a circular form or to a toroidal form in thepresence of neutralizing counterions is energetically favourable and is practically aspontaneous phenomenon.

Inhibition of DNA ejection from bacteriophage by Mg+2 counterions

The problem of inhibiting viral DNA ejection from bacteriophages by multivalent counterions, specifically Mg+2 counterions, is studied. Experimentally, it is known that MgSO4 salt has a strong and nonmonotonic effect on the amount of DNA ejected. There exists an optimal concentration at which the minimum amount of DNA is ejected from the virus. At lower or higher concentrations, more DNA is ejected from the capsid. We propose that this phenomenon is the result of DNA overcharging by Mg+2 multivalent counterions. As Mg+2 concentration increases from zero, the net charge of DNA changes from negative to positive. The optimal inhibition corresponds to the Mg+2 concentration where DNA is neutral. At lower/higher concentrations, DNA genome is charged. It prefers to be in solution to lower its electrostatic self-energy, which consequently leads to an increase in DNA ejection. By fitting our theory to available experimental data, the strength of DNA−DNA short range attraction energies, mediated by Mg+2, is found to be −0.004 kBT per nucleotide base. This and other fitted parameters agree well with known values from other experiments and computer simulations. The parameters are also in agreement qualitatively with values for tri- and tetravalent counterions.

Association of a Cylindrical Polyelectrolyte Brush with Tetravalent Counterions

Cylindrical poly(styrene sulfonate) brushes were combined with a tetravalent double-DABCO based counterion. With increasing addition of counterion, hydrodynamic radius and radius of gyration decrease and AFMreveals a conformation change from wormlike to curled structures. Rg/Rh changes from 1.3 to 0.9. Above charge stoichiometry, brushes become interconnected into finite size assemblies, which are stable in aqueous solution for charge ratios (ratio of the molar concentration of charged counterion groups to the molar concentration of charged monomer units of the polymer brush) 1 < l < 1.2. They are compact and consist of the brushes in curled (bent) conformation, which is in difference to network-like aggregates from cylindrical poly(styrene sulfonate) brushes with tetravalent porphyrin counterions (Gröhn et al. Macromolecules 2009) and to a wormlike - bent conformation - helix transition found for another brush counterion system (Müller et al. Soft Matter 2009).

Reentrant Behavior of Divalent-Counterion-Mediated DNA-DNA Electrostatic Interaction

The problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulation. Although divalent counterions cannot condense free DNA molecules in solution, we show that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetravalent counterions. DNA-DNA interaction is strongly repulsive at small or large counterion concentration and is negligible or slightly attractive for a concentration in between. Implications of our results to experiments of DNA ejection from bacteriophages are discussed. The quantitative result serves to understand electrostatic effects in other experiments involving DNA and divalent counterions.

Association of DNA with Multivalent Organic Counterions: From Flowers to Rods and Toroids

In this study, complexes of DNA with different organic di- and tetravalent counterions were systematically investigated in solution and on a surface. The complexation behavior was studied by dynamic light scattering, static light scattering, atomic force microscopy, analytical ultracentrifugation, and UV-vis spectroscopy. Results show that both divalent and tetravalent counterions can induce the formation of DNA complexes. Divalent counterions cause aggregation only at high counterion excess, with charge ratios of 50:1 for supercoiled DNA and 200:1 for linear DNA, while for different tetravalent counterions aggregation is already observed for charge ratios of about 1:1. Flower-like aggregates are observed with divalent counterions. For a tetravalent perylene based counterion, a transition from flower-like aggregates at low charge ratios to toroids and rods at high charge ratios is observed. A transition regime for intermediate charge ratios is found. The influence of concentration, added salt, and preparation method is also discussed. It is concluded that it is the interplay of electrostatics and component architectures that directs the structure formation.

Phase Behavior of Cetyltrimethylammonium Surfactants with Oligo Carboxylate Counterions Mixed with Water and Decanol: Attraction between Charged Planes or Spheres with Oligomeric Counterions

Cetyltrimethylammonium surfactants with a range of oligo carboxylate anions bearing 2, 3, or 4 negative charges have been synthesized, and their respective behaviors in binary mixtures with water and in ternary mixtures with added decanol have been investigated. In binary mixtures with water, all surfactants formed nearly spherical micelles at high water contents; however, the interactions between micelles varied strongly with the number of charges in the counterion. Micelles with divalent counterions were generally miscible with water, whereas micelles with tri- or tetravalent counterions demixed in one concentrated and one dilute phase. Addition of decanol resulted in all cases in the appearance of a lamellar phase, and all investigated oligo carboxylate anions (di-, tri-, and tetravalent) gave rise to a strong attraction between the lamellar planes, resulting in a limited swelling (up to 35-40 wt % water) of the lamellar phase in contact with excess water. These experiments confirm the theoretically predicted influence of aggregate geometry (spheres or planes) on the attraction between colloidal aggregates neutralized by multivalent counterions. Further addition of decanol resulted in the appearance of a second birefringent phase in equilibrium with the lamellar phase. SWAXS showed this phase to be lamellar and to display short-range order that disappeared upon heating. This phase is identified as a lamellar gel phase (Lbeta-phase).

Chain Morphology, Swelling Exponent, Persistence Length, Like-Charge Attraction, and Charge Distribution around a Chain in Polyelectrolyte Solutions: Effects of Salt Concentration and Ion Size Studied by Molecular Dynamics Simulations

Properties of polyelectrolytes in tetravalent salt solutions are intensively investigated by a coarse-grained model. The concentration of salt and the size of tetravalent counterions are found playing a decisive role on chain properties. If the size of tetravalent counterions is compatible with the one of monomers, the chains show extended structures at low and at high salt concentrations, whereas at intermediate salt concentrations, they acquire compact and prolate structures. The swelling exponent of a chain against salt concentration behaves in an analogous way as the morphological quantities. Under certain condition, the electrostatics gives a negative contribution to the persistence length, in companion with a salt-induced mechanical instability of polyelectrolytes. Nearly at the same moment, it appears like-charge attraction between chains. The equal size of the tetravalent ions and the monomers is the optimal condition to attain the strongest attraction between chains and the most compact chain structure. Moreover, the ions form a multilayer organization around a chain, and thus, the integrated charge distribution reveals an oscillatory behavior. The results suggest that charge inversion has no direct connection with redissolution of polyelectrolytes at high salt concentrations.

Linear polyelectrolytes in tetravalent salt solutions

The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.

DNA condensation and redissolution: interaction between overcharged DNA molecules

The effective DNA–DNA interaction force is calculated by computer simulations withexplicit tetravalent counterions and monovalent salt. For overcharged DNA molecules, theinteraction force shows a double-minimum structure. The positions and depths of theseminima are regulated by the counterion density in the bulk. Using two-dimensional latticesums and free energy perturbation theories, the coexisting phases for DNA bundles arecalculated. A DNA condensation and redissolution transition and a stable mesocrystal withan intermediate lattice constant for high counterion concentration are obtained.

Effect of Chain Stiffness on Polyelectrolyte Condensation

The effect of adding tetravalent counterions to polyelectrolytes of varying stiffness is investigated by a flat histogram Monte Carlo technique that is capable of giving the free energy of the system by direct simulation. The ensemble average of the polyelectrolyte size decreases with the amount of added salt for all chain stiffness. When examining the size distribution functions, flexible chains have narrow end-to-end distance distribution functions for all amounts of added salt. The distribution functions for semiflexible polyelectrolytes are always broader because such chains fluctuate between stretched and collapsed conformations. For stiff chains, the distribution functions show double maxima, which reflect the fact that individual chains prefer to be in elongated or compact toroid conformations, but not inbetween. This coexistence between compact and elongated conformations for stiff polyelectrolytes, when multivalent salt is added, is manifested in force-extension curves which exhibit a plateau regime in which the chain size changes markedly at a constant force.

Influence of Mixed and Multivalent Counterions in Overcharging of DNA-like Spherocylindrical Macroions

The influence of multivalent and mixed valency counterions on the ground-state energetics of overscreening of a core DNA-like model (sphero)cylindrical macroion is investigated using an earlier developed energy minimization numerical simulation algorithm. The effects of mono-, di-, tri-, and tetravalent counterions, and mixed valency (mono- plus di-) counterions are compared and contrasted. It is seen that the depth of the minimum in the excess ground-state energy (over the neutral reference state) versus the number of overcharging counterions increases as counterion valency changes from mono- to tetra- testifying to the efficiency of the overcharging process due to multivalent counterions. The influence of (i) the presence of mixed valency counterions and (ii) counterion size on the energetics is also investigated.

Higher-order assembly of microtubules by counterions: from hexagonal bundles to living necklaces.

Cellular factors tightly regulate the architecture of bundles of filamentous cytoskeletal proteins, giving rise to assemblies with distinct morphologies and physical properties, and a similar control of the supramolecular organization of nanotubes and nanorods in synthetic materials is highly desirable. However, it is unknown what principles determine how macromolecular interactions lead to assemblies with defined morphologies. In particular, electrostatic interactions between highly charged polyelectrolytes, which are ubiquitous in biological and synthetic self-assembled structures, are poorly understood. We have used a model system consisting of microtubules (MTs) and multivalent cations to examine how microscopic interactions can give rise to distinct bundle phases in biological polyelectrolytes. The structure of these supramolecular assemblies was elucidated on length scales from subnanometer to micrometer with synchrotron x-ray diffraction, transmission electron microscopy, and differential interference contrast microscopy. Tightly packed hexagonal bundles with controllable diameters were observed for large trivalent, tetravalent, and pentavalent counterions. Unexpectedly, in the presence of small divalent cations, we have discovered a living necklace bundle phase, comprised of 2D dynamic assemblies of MTs with linear, branched, and loop topologies. This new bundle phase is an experimental example of nematic membranes. The morphologically distinct MT assemblies give insight into general features of bundle formation and may be used as templates for miniaturized materials with applications in nanotechnology and biotechnology.

Simple Simulations of DNA Condensation

Molecular dynamics simulations of a simple, bead-spring model of semiflexible polyelectrolytes such as DNA are performed. All charges are explicitly treated. Starting from extended, noncondensed conformations, condensed structures form in the simulations with tetravalent or trivalent counterions. No condensates form or are stable for divalent counterions. The mechanism by which condensates form is described. Briefly, condensation occurs because electrostatic interactions dominate entropy, and the favored coulombic structure is a charge-ordered state. Condensation is a generic phenomenon and occurs for a variety of polyelectrolyte parameters. Toroids and rods are the condensate structures. Toroids form preferentially when the molecular stiffness is sufficiently strong.